Finite Group Databasebeta

← #7680806

Subgroups — #7680806

Order 512.

5030 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59855C214yesmaximal, complemented
2#59248C212yesmaximal, complemented
3#59245C212yesmaximal, complemented
4#59244C212yesmaximal, complemented
5#59234C212yesmaximal, complemented
6#59134C214yesmaximal, complemented
7#45065C214yesmaximal, complemented
8#45037C214yesmaximal, complemented
9#43151C218yesmaximal, complemented
10#39295C214yesmaximal, complemented
11#39294C214yesmaximal, complemented
12#39159C212yesmaximal, complemented
13#39158C212yesmaximal, complemented
14#36480C212yesmaximal, complemented
15#36473C212yesmaximal, complemented
16#35592C212yesmaximal
17#35545C212yesmaximal, complemented
18#35280C211yesmaximal, characteristic, complemented
19#35267C212yesmaximal, complemented
20#34947C211yesmaximal, characteristic, complemented
21C2×#2551C211yesmaximal, characteristic, complemented
22#34216C212yesmaximal, complemented
23#34213C211yesmaximal, characteristic, complemented
24#34188C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic
27C2×#556C2214yes—
28C2×#537C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2863C2214yes—
35#2860C2214yes—
36#2857C2212yes—
37#2857C2212yes—
38#2800C2218yes—
39#2789C2218yes—
40#2788C2218yes—
41#2776C2218yes—
42#2775C2218yes—
43#2759C2218yes—
44#2758C2218yes—
45#2745C2218yes—
46#2716C2218yes—
47#2716C2218yes—
48#2715C2218yes—
49#2700C2218yes—
50#2645C2214yes—
51#2644C2214yes—
52#2629C2214yes—
53#2605C2218yes—
54#2604C2218yes—
55#2599C2218yes—
56#2594C2218yes—
57#2591C2218yes—
58#2588C2218yes—
59#2582C2212yes—
60#2582C2212yes—
61#2568C2214yes—
62#2568C2211yescharacteristic
63#2567C2211yescharacteristic
64#2566C2212yes—
65#2565C2212yes—
66#2564C2214yes—
67#2563C2211yescharacteristic
68#2551C2214yes—
69#2551C2212yes—
70#2551C2212yes—
71#2551C2212yes—
72#2551C2214yes—
73#2551C2212yes—
74#2547C2214yes—
75#2545C2218yes—
76#2542C2211yescharacteristic
77#2538C2212yes—
78#2538C2212yes—
79#2525C2218yes—
80#2521C2218yes—
81#2514C2214yes—
82#2514C2214yes—
83#2513C2214yes—
84#2512C2214yes—
85#2511C2214yes—
86#2510C2218yes—
87#2510C2218yes—
88#2509C2214yes—
89#2497C2214yes—
90#2497C2214yes—
91#2496C2214yes—
92#2496C2214yes—
93#2495C2214yes—
94#2495C2214yes—
95#2494C2214yes—
96#2494C2214yes—
97#2494C2214yes—
98#2492C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2492C2214yes—
102#2492C2214yes—
103#2492C2214yes—
104#2491C2214yes—
105#2491C2214yes—
106#2491C2214yes—
107#2491C2214yes—
108#2485C2214yes—
109#2481C2218yes—
110#2481C2218yes—
111#2474C2218yes—
112#2469C2218yes—
113#2465C2218yes—
114#2446C2218yes—
115#2439C2214yes—
116#2439C2214yes—
117#2436C2218yes—
118#2421C2214yes—
119#2417C2212yes—
120#2417C2212yes—
121#2417C2214yes—
122#2417C2214yes—
123#2415C2214yes—
124#2396C2214yes—
125C2×#395C2214yes—
126#2370C2214yes—
127#2369C2214yes—
128#2369C2214yes—
129#2369C2212yes—
130#2365C2214yes—
131#2365C2214yes—
132#2365C2214yes—
133#2365C2212yes—
134#2362C2214yes—
135#2357C2212yes—
136#2356C2212yes—
137#2355C2214yes—
138#2355C2211yescharacteristic
139#2355C2211yescharacteristic
140#2355C2212yes—
141#2355C2212yes—
142#2355C2212yes—
143#2354C2211yescharacteristic
144#2354C2211yescharacteristic
145#2354C2212yes—
146#2354C2212yes—
147#2353C2214yes—
148#2352C2212yes—
149#2352C2212yes—
150#2352C2214yes—
151#2352C2214yes—
152Q8×C4⋊C4C2212yes—
153#2347C2214yes—
154#2345C2218yes—
155Q8×C22⋊C4C2218yes—
156#2331C2214yes—
157#2331C2214yes—
158#2329C2214yes—
159#2325C2214yes—
160#2324C2212yes—
161#2324C2212yes—
162#2323C2212yes—
163#2323C2212yes—
164#2317C2212yes—
165#2316C2211yescharacteristic
166#2316C2212yes—
167#2314C2214yes—
168#2311C2212yes—
169#2311C2212yes—
170#2311C2211yescharacteristic
171#2311C2211yescharacteristic
172C4×C4⋊Q8C2214yes—
173C4×C4⋊Q8C2214yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2214yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2214yes—
182#2298C2214yes—
183#2297C2212yes—
184#2297C2212yes—
185C2×#389C2212yes—
186C2×#389C2212yes—
187#2285C2211yescharacteristic
188#2285C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191C2×#384C2211yescharacteristic
192#2283C2212yes—
193#2274C2212yes—
194#2274C2212yes—
195C4×#117C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×Q8C2314yes—
202#556—416no—
203#537—28no—
204#533—28no—
205C2×C4⋊Q8—216no—
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2318yes—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#124C2318yes—
220C2×#124C2318yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C4×#41—28no—
233C4×#41—28no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2318yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2318yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276#401C2318yes—
277#401C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#399C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#395C2314yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#394C2318yes—
310#394C2318yes—
311#393C2314yes—
312#393C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#391C2318yes—
317#391C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2312yes—
329#391C2314yes—
330#391C2318yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#386C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#383C2318yes—
441#383C2318yes—
442#383C2314yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2312yes—
450#382C2314yes—
451#381C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2318yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2314yes—
471#380C2312yes—
472#380C2314yes—
473#380C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521#376C2314yes—
522C2×#95C2312yes—
523C2×#95C2312yes—
524C2×#95C2314yes—
525C43C2314yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—24no—
531C2×#41—24no—
532C22×Q8—216no—
533C22×Q8—48no—
534C22×Q8—84no—
535C22×Q8C2412yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2418yes—
539C22×Q8C2412yes—
540C22×Q8C2418yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C4⋊Q8—216no—
561C4⋊Q8—216no—
562C4⋊Q8—216no—
563C4⋊Q8—216no—
564C4⋊Q8—216no—
565C4⋊Q8—24no—
566C4⋊Q8—24no—
567C4⋊Q8—48no—
568C4⋊Q8—416no—
569#126—416no—
570#126—416no—
571#125—28no—
572#124—416no—
573#124—88no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—28no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—48no—
581C22⋊Q8—84no—
582#121—216no—
583#121—28no—
584#121—28no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—48no—
592C4×Q8—416no—
593C4×Q8—88no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—48no—
603#117—24no—
604#117—24no—
605#117—28no—
606#117—28no—
607#117—28no—
608#117—28no—
609#117—28no—
610#117—28no—
611#117—48no—
612#117—84no—
613C2×C4⋊C4—216no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—82no—
621C2×C4⋊C4#4118yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C42—28no—
700C2×C42—28no—
701C2×C42—28no—
702C2×C42—44no—
703C2×C42#4118yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2418yes—
720C2×C42C2418yes—
721C2×C42C2418yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2512yes—
775C24C2512yes—
776C24C2511yescharacteristic
777#41—416no—
778#41—416no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—216no—
785C2×Q8—24no—
786C2×Q8—216no—
787C2×Q8—24no—
788C2×Q8—216no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—48no—
793C2×Q8—42no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—42no—
797C2×Q8—832no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—28no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—44no—
812C2×D4—44no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—41no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4C2×#4114yes—
850C22×C4C2×#4114yes—
851C22×C4C2×#4118yes—
852C22×C4C2×#4114yes—
853C22×C4C2×#4114yes—
854C22×C42−1+414yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2518yes—
869C22×C4C2511yescharacteristic
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C4⋊C4—216no—
879C4⋊C4—216no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—28no—
900C4⋊C4—216no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C4⋊C4—48no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4C2×#4118yes—
926C4⋊C4C2×#4118yes—
927C4⋊C4H(5,𝔽2)14yes—
928C4⋊C42−1+414yes—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—28no—
966C42—28no—
967C42—28no—
968C42—28no—
969C42—28no—
970C42—44no—
971C42—44no—
972C42—48no—
973C42—48no—
974C42—48no—
975C42—44no—
976C42—48no—
977C42C2×#4114yes—
978C42C2×#4114yes—
979C42C2×#4114yes—
980C42C2×#4114yes—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23C22×#4112yes—
1000C23C22×#4112yes—
1001C23C2×2−1+412yes—
1002C23C2611yescharacteristic
1003Q8—432no—
1004Q8—44no—
1005Q8—44no—
1006Q8—48no—
1007Q8—84no—
1008Q8—816no—
1009D4—48no—
1010D4—48no—
1011D4—44no—
1012D4—44no—
1013D4—88no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—28no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—28no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—44no—
1070C2×C4—48no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—84no—
1080C2×C4—88no—
1081C2×C4#556116yescomplemented
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4118yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C2×H(5,𝔽2)14yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×2−1+414yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4C2×2−1+412yes—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22C2×#55614yes—
1118C22C23×#4111yescharacteristic
1119C22C23×#4111yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22H(7,𝔽2)11yescharacteristic
1124C222−1+611yescharacteristic
1125C4—28no—
1126C4—24no—
1127C4—24no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—42no—
1132C4—48no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—44no—
1137C4—42no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4C2×#55614yes—
1146C4C2×#55614yes—
1147C4#351114yes—
1148C2—24no—
1149C2—82no—
1150C2—82no—
1151C2C22×#55611yescharacteristic
1152C2C2×#351111yescharacteristic
1153C2#6285611yescharacteristic
1154C2#6291311yescharacteristic
1155C2#6294311yescharacteristic
1156C2#6298311yescharacteristic
1157C2#6299811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59855C2semidirect
2. #59248C2semidirect
3. #59245C2semidirect
4. #59244C2semidirect
5. #59234C2semidirect
6. #59134C2semidirect
7. #45065C2semidirect
8. #45037C2semidirect
9. #43151C2semidirect
10. #39295C2semidirect
11. #39294C2semidirect
12. #39159C2semidirect
13. #39158C2semidirect
14. #36480C2semidirect
15. #36473C2semidirect
17. #35545C2semidirect
18. #35280C2semidirect
19. #35267C2semidirect
20. #34947C2semidirect
21. C2×#2551C2semidirect
22. #34216C2semidirect
23. #34213C2semidirect
24. #34188C2semidirect
25. #34121C2semidirect
1081. C2×C4#556semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598552
#592482
#592452
#592442
#592342
#591342
#450652
#450372
#431512
#392952
#392942
#391592
#391582
#364802
#364732
#355922
#355452
#352802
#352672
#349472
C2×#25512
#342162
#342132
#341882
#341212
C4×#5372